arXiv subjects

Mark R. Krumholz

Publications and source records attributed to Mark R. Krumholz.

At least 163 records · Page 9Linked to original sources

arXiv2018

Dark Molecular Gas in Simulations of z~0 Disc Galaxies

The $\rm H_2$ mass of molecular clouds has traditionally been traced by the CO(J=1-0) rotational transition line. This said, CO is relatively easily photodissociated, and can also be destroyed by cosmic rays, thus rendering some fraction of molecular gas to be "CO-dark". We investigate the amount and physical properties of CO-dark gas in two $z \sim 0$ disc galaxies, and develop predictions for the expected intensities of promising alternative tracers ([CI 609 $μ$m and [CII] 158 $μ$m emission). We do this by combining cosmological zoom simulations of disc galaxies with thermal-radiative-chemical equilibrium interstellar medium (ISM) calculations to model the predicted H~\textsc{i} and $\rm H_2$ abundances and CO(J=1-0), [CI] 609 $μ$m and [CII] 158 $μ$m emission properties. Our model treats the ISM as a collection of radially stratified clouds whose properties are dictated by their volume and column densities, the gas-phase metallicity, and the interstellar radiation field and cosmic ray ionization rates. Our main results follow. Adopting an observationally motivated definition of CO-dark gas, i.e. $\rm H_2$ gas with $W_{\rm CO} < 0.1 $ K-km/s, we find that a significant amount ($> 50\%$) of the total $\rm H_2$ mass lies in CO-dark gas, most of which is diffuse gas, poorly shielded due to low dust column density. The CO-dark molecular gas tends to be dominated by [CII], though [CI] also serves as a bright tracer of the dark gas in many instances. At the same time, [CII] also tends to trace neutral atomic gas. As a result, when we quantify the conversion factors for the three carbon-based tracers of molecular gas, we find that [CI] suffers the least contamination from diffuse atomic gas, and is relatively insensitive to secondary parameters.

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arXiv2018

SLUG IV: A Novel Forward-Modelling Method to Derive the Demographics of Star Clusters

We describe a novel method for determining the demographics of a population of star clusters, for example distributions of cluster mass and age, from unresolved photometry. This method has a number of desirable properties: it fully exploits all the information available in a data set without any binning, correctly accounts for both measurement error and sample incompleteness, naturally handles heterogenous data (for example fields that have been imaged with different sets of filters or to different depths), marginalises over uncertain extinctions, and returns the full posterior distributions of the parameters describing star cluster demographics. We demonstrate the method using mock star cluster catalogs and show that our method is robust and accurate, and that it can recover the demographics of star cluster populations significantly better than traditional fitting methods. For realistic sample sizes, our method is sufficiently powerful that its accuracy is ultimately limited by the accuracy of the underlying physical models for stellar evolution and interstellar dust, rather than by statistical uncertainties. Our method is implemented as part of the Stochastically Lighting Up Galaxies (SLUG) stellar populations code, and is freely available.

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arXiv2018

Radiation Pressure Limits on the Star Formation Efficiency and Surface Density of Compact Stellar Systems

The large columns of dusty gas enshrouding and fuelling star-formation in young, massive stellar clusters may render such systems optically thick to radiation well into the infrared. This raises the prospect that both "direct" radiation pressure produced by absorption of photons leaving stellar surfaces and "indirect" radiation pressure from photons absorbed and then re-emitted by dust grains may be important sources of feedback in such systems. Here we evaluate this possibility by deriving the conditions under which a spheroidal, self-gravitating, mixed gas-star cloud can avoid catastrophic disruption by the combined effects of direct and indirect radiation pressure. We show that radiation pressure sets a maximum star cluster formation efficiency of $ε_{\rm max} \sim 0.9$ at a (very large) gas surface density of $\sim 10^5 M_\odot$ pc$^{-2} (Z_\odot/Z) \simeq 20$ g cm$^{-2} (Z_\odot/Z)$, but that gas clouds above this limit undergo significant radiation-driven expansion during star formation, leading to a maximum stellar surface density very near this value for all star clusters. Data on the central surface mass density of compact stellar systems, while sparse and partly confused by dynamical effects, are broadly consistent with the existence of a metallicity-dependent upper-limit comparable to this value. Our results imply that this limit may preclude the formation of the progenitors of intermediate-mass black holes for systems with $Z \gtrsim 0.2 Z_\odot$.

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arXiv2018

Numerical Calibration of the HCN$-$Star Formation Correlation

HCN(1$-$0) emission traces dense gas and correlates very strongly with star formation rates (SFRs) on scales from small Milky Way clouds to whole galaxies. The observed correlation offers strong constraints on the efficiency of star formation in dense gas, but quantitative interpretation of this constraint requires a mapping from HCN emission to gas mass and density. In this paper we provide the required calibration by postprocessing high-resolution simulations of dense, star-forming clouds to calculate their HCN emission ($L_{\rm HCN}$) and to determine how that emission is related to the underlying gas density distribution and star formation efficiency. We find that HCN emission traces gas with a luminosity-weighted mean number density of $0.8-1.7 \times 10^4\,{\rm cm}^{-3}$ and that HCN luminosity is related to mass of dense gas of $\gtrsim 10^4\,{\rm cm}^{-3}$ with a conversion factor of $α_{\rm HCN} \approx 14\,\rm M_{\odot}/(K\,km\,s^{-1}\,{pc}^2)$. We also measure a new empirical relationship between the SFR per global mean freefall time ($ε_{\rm ff}$) and the SFR$-$HCN relationship, ${\rm SFR}/L_{\rm HCN} = 2.0 \times 10^{-7}\,(ε_{\rm ff}/0.01)^{1.1}\,\rm M_{\odot}\,{yr}^{-1}/(K\,km\,s^{-1}\,{pc}^2)$. The observed SFR$-$HCN correlation strongly constrains $ε_{\rm ff} \approx 1\%$ with a factor of $\sim 3$ systematic uncertainty. The scatter in $ε_{\rm ff}$ from cloud to cloud within the Milky Way is a factor of a few. We conclude that $L_{\rm HCN}$ is an effective tracer of dense gas and that the IR$-$HCN correlation is a significant diagnostic of the microphysics of star formation in dense gas.

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arXiv2018

Short-lived radioisotopes in meteorites from Galactic-scale correlated star formation

Meteoritic evidence shows that the Solar system at birth contained significant quantities of short-lived radioisotopes (SLRs) such as 60Fe and 26Al (with half-lives of 2.6 and 0.7 Myr respectively) produced in supernova explosions and in the Wolf-Rayet winds that precede them. Proposed explanations for the high SLR abundance include formation of the Sun in a supernova-triggered collapse or in a giant molecular cloud (GMC) that was massive enough to survive multiple supernovae (SNe) and confine their ejecta. However, the former scenario is possible only if the Sun is a rare outlier among massive stars, while the latter appears to be inconsistent with the observation that 26Al is distributed with a scale height significantly larger than GMCs. In this paper, we present a high-resolution chemo-hydrodynamical simulation of the entire Milky-Way Galaxy, including stochastic star formation, HII regions, SNe, and element injection, that allows us to measure for the distribution of 60Fe/56Fe and 26Al/27Al ratios over all stars in the Galaxy. We show that the Solar System's abundance ratios are well within the normal range, but that SLRs originate neither from triggering nor from confinement in long-lived clouds as previously conjectured. Instead, we find that SLRs are abundant in newborn stars because star formation is correlated on galactic scales, so that ejecta preferentially enrich atomic gas that will subsequently be accreted onto existing GMCs or will form new ones. Thus new generations of stars preferentially form in patches of the Galaxy contaminated by previous generations of stellar winds and supernovae.

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arXiv2018

Theoretical predictions for IMF diagnostics in UV spectroscopy of star clusters

We explore the possibility of using UV spectroscopy in combination with broad-band photometry as diagnostic tools for understanding the shape of the Initial Mass Function (IMF) in unresolved stellar populations. Building on our previous work, we extend the Stochastically Lighting Up Galaxies code (slug) to include a high-resolution UV spectral synthesiser and equivalent width calculation capabilities. We first gain a qualitative understanding of how UV spectral features behave as the parameters that define a star cluster in slug (mass, age, extinction, and IMF slope alpha) are changed. We then exploit Bayesian inference techniques to recover the alpha values for clusters simulated with slug, using mock observations of these clusters comprised of broad-band photometry and equivalent width measurements of a selection of UV spectral features. We find some improvement when compared to attempts using broad-band photometry alone (with the interquartile range of the alpha posterior PDF shrinking by 32%), although we still do not yet fully break the known degeneracy between the cluster mass and alpha. Finally, we make predictions about how effective real observations will be by quantifying our ability to constrain alpha as a function of limiting equivalent width. We find that observations sensitive to a modest equivalent width of 9 A are sufficient to improve the recovery of the IMF slope parameter by 32% (interquartile range of posterior PDF median residuals), moving to 39% when we include all the significant spectral features in the wavelength range 900-3000 A.

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arXiv2018

Resolution Requirements and Resolution Problems in Simulations of Radiative Feedback in Dusty Gas

In recent years a number of authors have introduced methods to model the effects of radiation pressure feedback on flows of interstellar and intergalactic gas, and have posited that the forces exerted by stars' radiation output represents an important feedback mechanism capable of halting accretion and thereby regulating star formation. However, numerical simulations have reached widely varying conclusions about the effectiveness of this feedback. In this paper I show that much of the divergence in the literature is a result of failure to obey an important resolution criterion: whether radiation feedback is able to reverse an accretion flow is determined on scales comparable to the dust destruction radius, which is $\lesssim 1000$ AU even for the most luminous stellar sources. Simulations that fail to resolve this scale can produce unphysical results, in many cases leading to a dramatic overestimate of the effectiveness of radiation feedback. Most published simulations of radiation feedback on molecular cloud and galactic scales fail to satisfy this condition. I show how the problem can be circumvented by introducing a new subgrid model that explicitly accounts for momentum balance on unresolved scales, making it possible to simulate dusty accretion flows safely even at low resolution.

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arXiv2018

Mixing of metals during star cluster formation: statistics and implications for chemical tagging

Ongoing surveys are in the process of measuring the chemical abundances in large numbers of stars, with the ultimate goal of reconstructing the formation history of the Milky Way using abundances as tracers. However, interpretation of these data requires that we understand the relationship between stellar distributions in chemical and physical space, i.e., how similar in chemical abundance do we expect a pair of stars to be as a function of the distance between their formation sites. We investigate this question by simulating the gravitational collapse of a turbulent molecular cloud extracted from a galaxy-scale simulation, seeded with chemical inhomogeneities with different initial spatial scales. We follow the collapse from galactic scales down to resolutions scales of $\approx 10^{-3}$ pc, and find that, during this process, turbulence mixes the metal patterns, reducing the abundance scatter initially present in the gas by an amount that depends on the initial scale of inhomogeneity of each metal field. However, we find that regardless of the initial spatial structure of the metals at the onset of collapse, the final stellar abundances are highly correlated on distances below a few pc, and nearly uncorrelated on larger distances. Consequently, the star formation process defines a natural size scale of $\sim 1$ pc for chemically-homogenous star clusters, suggesting that any clusters identified as homogenous in chemical space must have formed within $\sim 1$ pc of one another. However, in order to distinguish different star clusters in chemical space, observations across multiple elements will be required, and the elements that are likely to be most efficient at separating distinct clusters in chemical space are those whose correlation length in the ISM is of order tens of pc, comparable to the sizes of individual molecular clouds.

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arXiv2018

Isothermal Fragmentation: Is there a low-mass cut-off?

The evolution of self-gravitating clouds of isothermal gas forms the basis of many star formation theories. Therefore it is important to know under what conditions such a cloud will undergo homologous collapse into a single, massive object, or will fragment into a spectrum of smaller ones. And if it fragments, do initial conditions (e.g. Jeans mass, sonic mass) influence the mass function of the fragments, as predicted by many theories of star formation? In this paper we show that the relevant parameter separating homologous collapse from fragmentation is not the Mach number of the initial turbulence (as suspected by many), but the infall Mach number $\mathcal{M}_{\rm infall}\sim\sqrt{G M/(R c_s^2)}$, equivalent to the number of Jeans masses in the initial cloud $N_J$. We also show that fragmenting clouds produce a power-law mass function with slopes close to the expected -2 (i.e. equal mass in all logarithmic mass intervals). However, the low-mass cut-off of this mass function is entirely numerical; the initial properties of the cloud have no effect on it. In other words, if $\mathcal{M}_{\rm infall}\gg 1$, fragmentation proceeds without limit to masses much smaller than the initial Jeans mass.

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arXiv2018

The Maximum Flux of Star-Forming Galaxies

The importance of radiation pressure feedback in galaxy formation has been extensively debated over the last decade. The regime of greatest uncertainty is in the most actively star-forming galaxies, where large dust columns can potentially produce a dust-reprocessed infrared radiation field with enough pressure to drive turbulence or eject material. Here we derive the conditions under which a self-gravitating, mixed gas-star disc can remain hydrostatic despite trapped radiation pressure. Consistently taking into account the self-gravity of the medium, the star- and dust-to-gas ratios, and the effects of turbulent motions not driven by radiation, we show that galaxies can achieve a maximum Eddington-limited star formation rate per unit area $\dotΣ_{\rm *,crit} \sim 10^3 M_{\odot}$ pc$^{-2}$ Myr$^{-1}$, corresponding to a critical flux of $F_{\rm *,crit} \sim 10^{13} L_{\odot}$ kpc$^{-2}$ similar to previous estimates; higher fluxes eject mass in bulk, halting further star formation. Conversely, we show that in galaxies below this limit, our one-dimensional models imply simple vertical hydrostatic equilibrium and that radiation pressure is ineffective at driving turbulence or ejecting matter. Because the vast majority of star-forming galaxies lie below the maximum limit for typical dust-to-gas ratios, we conclude that infrared radiation pressure is likely unimportant for all but the most extreme systems on galaxy-wide scales. Thus, while radiation pressure does not explain the Kennicutt-Schmidt relation, it does impose an upper truncation on it. Our predicted truncation is in good agreement with the highest observed gas and star formation rate surface densities found both locally and at high redshift.

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arXiv2018

A Unified Model for Galactic Discs: Star Formation, Turbulence Driving, and Mass Transport

We introduce a new model for the structure and evolution of the gas in galactic discs. In the model the gas is in vertical pressure and energy balance. Star formation feedback injects energy and momentum, and non-axisymmetric torques prevent the gas from becoming more than marginally gravitationally unstable. From these assumptions we derive the relationship between galaxies' bulk properties (gas surface density, stellar content, and rotation curve) and their star formation rates, gas velocity dispersions, and rates of radial inflow. We show that the turbulence in discs can be powered primarily by star formation feedback, radial transport, or a combination of the two. In contrast to models that omit either radial transport or star formation feedback, the predictions of this model yield excellent agreement with a wide range of observations, including the star formation law measured in both spatially resolved and unresolved data, the correlation between galaxies' star formation rates and velocity dispersions, and observed rates of radial inflow. The agreement holds across a wide range of galaxy mass and type, from local dwarfs to extreme starbursts to high-redshifts discs. We apply the model to galaxies on the star-forming main sequence, and show that it predicts a transition from mostly gravity-driven turbulence at high redshift to star formation-driven turbulence at low redshift. This transition, and the changes in mass transport rates that it produces, naturally explain why galaxy bulges tend to form at high redshift and discs at lower redshift, and why galaxies tend to quench inside-out.

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arXiv2018

Instability of Supersonic Cold Streams Feeding Galaxies II. Nonlinear Evolution of Surface and Body Modes of Kelvin-Helmholtz Instability

As part of our long-term campaign to understand how cold streams feed massive galaxies at high redshift, we study the Kelvin-Helmholtz instability (KHI) of a supersonic, cold, dense gas stream as it penetrates through a hot, dilute circumgalactic medium (CGM). A linear analysis (Paper I) showed that, for realistic conditions, KHI may produce nonlinear perturbations to the stream during infall. Therefore, we proceed here to study the nonlinear stage of KHI, still limited to a two-dimensional slab with no radiative cooling or gravity. Using analytic models and numerical simulations, we examine stream breakup, deceleration and heating via surface modes and body modes. The relevant parameters are the density contrast between stream and CGM ($δ$), the Mach number of the stream velocity with respect to the CGM ($M_{\rm b}$) and the stream radius relative to the halo virial radius ($R_{\rm s}/R_{\rm v}$). We find that sufficiently thin streams disintegrate prior to reaching the central galaxy. The condition for breakup ranges from $R_{\rm s} < 0.03 R_{\rm v}$ for $(M_{\rm b} \sim 0.75, δ\sim 10)$ to $R_{\rm s} < 0.003 R_{\rm v}$ for $(M_{\rm b} \sim 2.25, δ\sim 100)$. However, due to the large stream inertia, KHI has only a small effect on the stream inflow rate and a small contribution to heating and subsequent Lyman-$α$ cooling emission.

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arXiv2018

Dwarf Galaxies with Ionizing Radiation Feedback. I: Escape of Ionizing Photons

We describe a new method for simulating ionizing radiation and supernova feedback in the analogues of low-redshift galactic disks. In this method, which we call star-forming molecular cloud (SFMC) particles, we use a ray-tracing technique to solve the radiative transfer equation for ultraviolet photons emitted by thousands of distinct particles on the fly. Joined with high numerical resolution of 3.8 pc, the realistic description of stellar feedback helps to self-regulate star formation. This new feedback scheme also enables us to study the escape of ionizing photons from star-forming clumps and from a galaxy, and to examine the evolving environment of star-forming gas clumps. By simulating a galactic disk in a halo of 2.3e11 Msun, we find that the average escape fraction from all radiating sources on the spiral arms (excluding the central 2.5 kpc) fluctuates between 0.08% and 5.9% during a ~20 Myr period with a mean value of 1.1%. The flux of escaped photons from these sources is not strongly beamed, but manifests a large opening angle of more than 60 degree from the galactic pole. Further, we investigate the escape fraction per SFMC particle, f_esc(i), and how it evolves as the particle ages. We discover that the average escape fraction f_esc is dominated by a small number of SFMC particles with high f_esc(i). On average, the escape fraction from a SFMC particle rises from 0.27% at its birth to 2.1% at the end of a particle lifetime, 6 Myrs. This is because SFMC particles drift away from the dense gas clumps in which they were born, and because the gas around the star-forming clumps is dispersed by ionizing radiation and supernova feedback. The framework established in this study brings deeper insight into the physics of photon escape fraction from an individual star-forming clump, and from a galactic disk.

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arXiv2018

Dwarf Galaxies with Ionizing Radiation Feedback. II: Spatially-resolved Star Formation Relation

We investigate the spatially-resolved star formation relation using a galactic disk formed in a comprehensive high-resolution (3.8 pc) simulation. Our new implementation of stellar feedback includes ionizing radiation as well as supernova explosions, and we handle ionizing radiation by solving the radiative transfer equation rather than by a subgrid model. Photoheating by stellar radiation stabilizes gas against Jeans fragmentation, reducing the star formation rate. Because we have self-consistently calculated the location of ionized gas, we are able to make spatially-resolved mock observations of star formation tracers, such as H-alpha emission. We can also observe how stellar feedback manifests itself in the correlation between ionized and molecular gas. Applying our techniques to the disk in a galactic halo of 2.3e11 Msun, we find that the correlation between star formation rate density (estimated from mock H-alpha emission) and molecular hydrogen density shows large scatter, especially at high resolutions of <~ 75 pc that are comparable to the size of giant molecular clouds (GMCs). This is because an aperture of GMC size captures only particular stages of GMC evolution, and because H-alpha traces hot gas around star-forming regions and is displaced from the molecular hydrogen peaks themselves. By examining the evolving environment around star clusters, we speculate that the breakdown of the traditional star formation laws of the Kennicutt-Schmidt type at small scales is further aided by a combination of stars drifting from their birthplaces, and molecular clouds being dispersed via stellar feedback.

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arXiv2018

Metallicity Fluctuation Statistics in the Interstellar Medium and Young Stars. I. Variance and Correlation

The distributions of a galaxy's gas and stars in chemical space encodes a tremendous amount of information about that galaxy's physical properties and assembly history. However, present methods for extracting information from chemical distributions are based either on coarse averages measured over galactic scales (e.g., metallicity gradients) or on searching for clusters in chemical space that can be identified with individual star clusters or gas clouds on $\sim 1$ pc scales. These approaches discard most of the information, because in galaxies gas and young stars are observed to be distributed fractally, with correlations on all scales, and the same is likely to be true of metals. In this paper we introduce a first theoretical model, based on stochastically-forced diffusion, capable of predicting the multi-scale statistics of metal fields. We derive the variance, correlation function, and power spectrum of the metal distribution from first principles, and determine how these quantities depend on elements' astrophysical origin sites and on the large-scale properties of galaxies. Among other results, we explain for the first time why the typical abundance scatter observed in the interstellar media of nearby galaxies is $\approx 0.1$ dex, and we predict that this scatter will be correlated on spatial scales of $\sim 0.5-1$ kpc, and over time scales of $\sim 100-300$ Myr. We discuss the implications of our results for future chemical tagging studies.

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arXiv2018

The Effects of Magnetic Fields and Protostellar Feedback on Low-mass Cluster Formation

We present a large suite of simulations of the formation of low-mass star clusters. Our simulations include an extensive set of physical processes -- magnetohydrodynamics, radiative transfer, and protostellar outflows -- and span a wide range of virial parameters and magnetic field strengths. Comparing the outcomes of our simulations to observations, we find that simulations remaining close to virial balance throughout their history produce star formation efficiencies and initial mass function (IMF) peaks that are stable in time and in reasonable agreement with observations. Our results indicate that small-scale dissipation effects near the protostellar surface provide a feedback loop for stabilizing the star formation efficiency. This is true regardless of whether the balance is maintained by input of energy from large scale forcing or by strong magnetic fields that inhibit collapse. In contrast, simulations that leave virial balance and undergo runaway collapse form stars too efficiently and produce an IMF that becomes increasingly top-heavy with time. In all cases we find that the competition between magnetic flux advection toward the protostar and outward advection due to magnetic interchange instabilities, and the competition between turbulent amplification and reconnection close to newly-formed protostars renders the local magnetic field structure insensitive to the strength of the large-scale field, ensuring that radiation is always more important than magnetic support in setting the fragmentation scale and thus the IMF peak mass. The statistics of multiple stellar systems are similarly insensitive to variations in the initial conditions and generally agree with observations within the range of statistical uncertainty.

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arXiv2018

Radiation pressure in galactic disks: stability, turbulence, and winds in the single-scattering limit

The radiation force on dust grains may be dynamically important in driving turbulence and outflows in rapidly star-forming galaxies. Recent studies focus on the highly optically-thick limit relevant to the densest ultra-luminous galaxies and super star clusters, where reprocessed infrared photons provide the dominant source of electromagnetic momentum. However, even among starburst galaxies, the great majority instead lie in the so-called "single-scattering" limit, where the system is optically-thick to the incident starlight, but optically-thin to the re-radiated infrared. In this paper we present a stability analysis and multidimensional radiation-hydrodynamic simulations exploring the stability and dynamics of isothermal dusty gas columns in this regime. We describe our algorithm for full angle-dependent radiation transport based on the discontinuous Galerkin finite element method. For a range of near-Eddington fluxes, we show that the medium is unstable, producing convective-like motions in a turbulent atmosphere with a scale height significantly inflated compared to the gas pressure scale height and mass-weighted turbulent energy densities of $\sim 0.01-0.1$ of the midplane radiation energy density, corresponding to mass-weighted velocity dispersions of Mach number $\sim 0.5-2$. Extrapolation of our results to optical depths of $10^3$ implies maximum turbulent Mach numbers of $\sim20$. Comparing our results to galaxy-averaged observations, and subject to the approximations of our calculations, we find that radiation pressure does not contribute significantly to the effective supersonic pressure support in star-forming disks, which in general are substantially sub-Eddington. We further examine the time-averaged vertical density profiles in dynamical equilibrium and comment on implications for radiation-pressure-driven galactic winds.

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arXiv2017

The Observable Properties of Cool Winds from Galaxies, AGN, and Star Clusters. I. Theoretical Framework

Winds arising from galaxies, star clusters, and active galactic nuclei are crucial players in star and galaxy formation, but it has proven remarkably difficult to use observations of them to determine physical properties of interest, particularly mass fluxes. Much of the difficulty stems from a lack of a theory that links a physically-realistic model for winds' density, velocity, and covering factors to calculations of light emission and absorption. In this paper we provide such a model. We consider a wind launched from a turbulent region with a range of column densities, derive the differential acceleration of gas as a function of column density, and use this result to compute winds' absorption profiles, emission profiles, and emission intensity maps in both optically thin and optically thick species. The model is sufficiently simple that all required computations can be done analytically up to straightforward numerical integrals, rendering it suitable for the problem of deriving physical parameters by fitting models to observed data. We show that our model produces realistic absorption and emission profiles for some example cases, and argue that the most promising methods of deducing mass fluxes are based on combinations of absorption lines of different optical depths, or on combining absorption with measurements of molecular line emission. In the second paper in this series, we expand on these ideas by introducing a set of observational diagnostics that are significantly more robust that those commonly in use, and that can be used to obtain improved estimates of wind properties.

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